By Luigi Accardi, Wilhelm v. Waldenfels
Read or Download Quantum Probability and Applications II: Proceedings of a Workshop held in Heidelberg, West Germany, October 1-5, 1984 (Lecture Notes in Mathematics) PDF
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Extra resources for Quantum Probability and Applications II: Proceedings of a Workshop held in Heidelberg, West Germany, October 1-5, 1984 (Lecture Notes in Mathematics)
Is a strongly ^2 continuous Then P is a dense set of ^ ~ Si + Do' Pn i s an i n v a r i a n t i=1 conservative is associated a Markov process ~tO on S ( ~ ) s u b s p a c e f o r e tf~, and Markov s e m i g r o u p on C ( S ( ~ ' ~ ) ) . To i t there and one has ^ (etLf) (o) = E(f(~t)) for all f C C ( S ( ~ ) ) . Moreover ^ e tL ~ A f f ( S ( ~ ) ) = • oq0t and thus, by Theorem 4 e t~ (~) = o = ~ t = E(~) with ~(o) E o o~t, so that ~ C A f f ( S ( ~ ) ) . It would be very interesting to extend all of the above results to the case of more * general C -algebras.
11 ]. The above theorems give a connection between dynamical semigroups o n ~ diffusions on A u t J ~ . e. on pure states? The answer is yes. Let S ( ~ ) semigroup o n ~ . e. the set of pure states. ~ " a Markov process on S ( ~ ) , which carries De S ( ~ ) qt = ~ o X et ~s into ~e S ( ~ ) . Remark into itself, Let X e be as in Theorem 3. Let $ • the extreme boundary of S ( ~ ) and let ~t be a dynamical is an affine map from S ( ~ ) a qt is an affine map on S ( ~ ) . One has o = ~ t Thus the process qt in the state space S < ~ ) of A = E(q~).
Stochastic Univ. D. Stochastic Processes, Maps on the CAR Algebra , Limit of Reduced Quantum DILATIONS OF OPERATION VALUED STOCHASTIC PROCESSES A. BARCHIELLI and G. Operation valued stochastic processes. T. [l]). In this framework continual measurements can be consistently introduced in quantum mechanics. The first works on continual measurements are due to Davies, who treated the theory of counting processes under the name of "quantum stochastic processes" (a complete list of references is given in [1-3]).